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Abstract:
Thermally driven vertical convection (VC) - the flow in a box heated on one side and cooled on the other side, is investigated using direct numerical simulations with Rayleigh numbers over the wide range of 10^7<=Ra<=10^14 and a fixed Prandtl number Pr=10 in a two-dimensional convection cell with unit aspect ratio. It is found that the dependence of the mean vertical centre temperature gradient S on Ra shows three different regimes: in regime I (Ra<=5x10^10), S is almost independent of Ra; in the newly identified regime II (5x10^10<=Ra<=10^13), S first increases with increasing Ra (regime IIa), reaches its maximum and then decreases again (regime IIb); and in regime III (Ra > 1013), S again becomes only weakly dependent on Ra, being slightly smaller than in regime I. The transition from regime I to regime II is related to the onset of unsteady flows arising from the ejection of plumes from the sidewall boundary layers. The maximum of S occurs when these plumes are ejected over approximately half of the area (downstream) of the sidewalls. The onset of regime III is characterized by the appearance of layered structures near the top and bottom horizontal walls. The flow in regime III is characterized by a well-mixed bulk region owing to continuous ejection of plumes over large fractions of the sidewalls, and, as a result of the efficient mixing, the mean temperature gradient in the centre S is smaller than that of regime I. In the three different regimes, significantly different flow organizations are identified: in regime I and regime IIa, the location of the maximal horizontal velocity is close to the top and bottom walls; however, in regime IIb and regime III, banded zonal flow structures develop and the maximal horizontal velocity now is in the bulk region. The different flow organizations in the three regimes are also reflected in the scaling exponents in the effective power law scalings Nu-Raβ and Re-Raγ. Here, Nu is the Nusselt number and Re is the Reynolds number based on maximal vertical velocity (averaged over vertical direction). In regime I, the fitted scaling exponents (β ≈ 0.26 and γ ≈ 0.51) are in excellent agreement with the theoretical predictions of β=1/4 and γ=1/2 for laminar VC (Shishkina, Phys. Rev. E., vol. 93, 2016, 051102). However, in regimes II and III, β increases to a value close to 1/3 and γ decreases to a value close to 4/9. The stronger Ra dependence of Nu is related to the ejection of plumes and the larger local heat flux at the walls. The mean kinetic dissipation rate also shows different scaling relations with Ra in the different regimes.
